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For all U.S. students nationally who take the SAT, SAT Math scores are normally distributed with an average score of 500 and a population standard deviation of 125. A random sample of 100 students entering Whitmer College had an average SAT Math (SAT-M) score of 530.

The sample data can be used to test the claim that the mean SAT-M score of all Whitmer College students is different from the national mean SAT-M score.

Based on the given information and using the appropriate formula, calculate the test statistic for this hypothesis test. Round your answer to two decimal places.

Enter the numeric value of the test statistic in the space below:

Answer :

The test statistic for this hypothesis test is 2.40. This indicates that the sample mean SAT Math score of 530 for Whitmer College students is 2.40 standard deviations above the population mean of 500 for all U.S. students.

To calculate the test statistic for this hypothesis test, we use the formula for the z-score:

[tex]\[ z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}} \][/tex]

Where:

- [tex]\( \bar{x} \)[/tex] is the sample mean (average SAT Math score of Whitmer College students), which is 530.

- [tex]\( \mu \)[/tex] is the population mean (average SAT Math score of all U.S. students), which is 500.

- [tex]\( \sigma \)[/tex] is the population standard deviation, which is 125.

- [tex]\( n \)[/tex] is the sample size, which is 100.

Plugging in the values, we get:

[tex]\[ z = \frac{530 - 500}{\frac{125}{\sqrt{100}}} \][/tex]

[tex]\[ z = \frac{30}{\frac{125}{10}} \][/tex]

[tex]\[ z = \frac{30}{12.5} \][/tex]

[tex]\[ z = 2.4 \][/tex]

Rounding to two decimal places, the test statistic for this hypothesis test is 2.40.

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